Noise A 1-confidence interval for the persistence diagram consists of an estimate and such that The 1st Persistent Landscape (Bubenik, 2012) is the maximum contour of the triangles: We want a confidence band for .-Compute c, the 1-quantile of the bootstrapped .

We consider both ℓ0-penalized and ℓ0-constrained quantile regression estimators. For the estimator, we derive an exponential inequality on tail probability of excess prediction risk apply it to obtain non-asymptotic upper bounds mean-square parameter function estimation errors. also analogous results for estimator. The resulting rates convergence are nearly minimax-optimal same as those ℓ1-pena...

In using multiple regression methods for prediction, one often considers the linear combination of explanatory variables as an index. Seeking a single such index when here are responses is rather more complicated. One classical approach to use coefficients from leading Canonical Correlation. However, based on variances unable disaggregate by quantile effects, lack robustness, and rely normal as...

The purpose of regression analysis is to expose the relationship between a response variable and predictor variables. In real applications, the response variable cannot be predicted exactly from the predictor variables. Instead, the response for a fixed value of each predictor variable is a random variable. For this reason, we often summarize the behavior of the response for fixed values of the...